Lecture on Rational and Irrational Numbers

Introduction

• Welcome by Ajit: Welcome everyone, request to like and share the video.
• Today's topic: Rational and Irrational Numbers.
• Promise to clear all confusions.

New Features

• Preparation for NDA and IIT in Sukhoi.
• Registration open for classes 9 and 11.
• Scholarship exam on March 17th.

Number System

• Two parts of the number system:
  • Real Numbers
  • Imaginary Numbers
• Definition of Real Numbers:
  • These can be divided into natural, whole, integers, etc.
• Examples of Imaginary Numbers:
  • Like √-1 is called 'i'.

Definition of Rational Numbers

• Three main points of rational numbers:
  1. Any number can be written in the form p/q.
  2. p and q should be integers.
  3. The value of q should not be 0.
• Examples:
  • 2 = 2/1 (Rational Number)
  • -3 = -3/1 (Rational Number)
  • 3.5 = 35/10 (Rational Number)

Difference between Rational and Irrational Numbers

• All rational numbers are fractions, but not all fractions are rational numbers.
• In fractions, p and q are whole numbers, whereas in rational numbers they can be integers.

Examples of Division

• Examples like 7/8, 2157/625 etc. were given.
• Division of various numbers and their results.

Categories of Decimal Numbers

• Terminating Decimal: Ends at a certain point.
• Non-Terminating: Does not end.
  • Non-Terminating Repeating: Like 0.666…
  • Non-Terminating Non-Repeating: Like π

Irrational Numbers

• Definition of irrational numbers:
  • These are numbers that cannot be written in the form p/q.
  • Examples: √2, π etc.

Conclusion

• Basic concepts of rational and irrational numbers explained.
• Will help students solve their problems.
• More information in the next class.

Thank You

• Thanks to all students and assurance of meeting again tomorrow.
• Jai Hind!